One sample or independent samples t-test?

#1
Hello everyone :)

I have a problem with a mark I have received regarding my stats assignment.

The data was comparing management scores (scale variable) between countries (nominal variable with 7 categories)

One of the tasks was to "Test the null hypothesis that there are no significant differences in the mean overall management score between the UK and each of the other countries."

So as you see, the instruction did not specify whether one sample or independent samples t-test was meant to be run. I run one-sample t-test where I entered the test value as 2.848 (calculating mean management score for the UK was also one of the tasks).

Having received feedback, the teacher said that "When comparing two sample means from two different populations, use an independent sample t-test." so that what I did was wrong. And I don't quite understand why. In my understanding, independent samples t-test is run when there is a grouping variable which consists of two categorical, independent groups (i.e., a dichotomous variable). Such as gender (two groups: "males" or "females"), employment status (two groups: "employed" or "unemployed"), transport type (two groups: "bus" or "car"), smoker (two groups: "yes" or "no"), trial (two groups: "intervention" or "control").

Therefore in my understanding the country variable in our sample does not meet that criterion. Unless it was to be recoded into a dummy but I'm not sure if that's the right way to go about it?

Can you tell me what you think of this? That teacher is not a specialist in statistics so I have doubts about her judgement.

Thanks in advance :)
 

Dason

Ambassador to the humans
#2
Your teacher is right. If you do a one sample test and just compare against the sample mean for the UK then you ignore all the variability in the sample for UK.
 
#3
Your teacher is right. If you do a one sample test and just compare against the sample mean for the UK then you ignore all the variability in the sample for UK.
Thank you for your response Dason.

Still, can you tell me how it would technically work with running the independent samples t-test? Because I have tried to do that (in SPSS 25) and the grouping variable allows to define 2 groups. In my sample, the country variable has 7, so it doesn't even let me run the test?